2-
I4 1 III
0 2 4 6 8 10 12
Chain separation Ik 11
Figure 4-1.
14 16 18 20
Test results for the simple example of a bosonic chain. An MC simulation
with 2 104 sweeps and parameters M 21, a 1. The figure shows the
results for the expectation value F(k,1) ((qk q)2) where the spacing
Ik l1 is shown on x-axis. The two graphs share the x-axis and in the upper
plot the stems are MC results and the solid line is the exact answer for F(k, 1)
from Eqn. 4-10. The lower plot shows the residuals, meaning the difference
between the MC and exact results. By fitting the MC results to a functional
form as for F above we obtain M = 20.49 and a = 0.9926. Notice that
the difference plot has some structure. We believe that this is an indication
of correlation between MC errors along the chain, which is an effect we see
clearly on the lattice and shall discuss in more detail later.
our Lightcone World Sheet setup except with a different interaction. The Ising spin system
only has a local interaction. Although the Lightcone World Sheet interaction is also local,
we intend to treat the 1/p factors non-locally, i.e., we do not employ the local b, c ghosts
but instead put in the 1/p+ by hand making the interaction at least mildly non-local. The